Many lack the college degrees that employers are seeking. The jobless rate for veterans who served at any time since September 2001 was 13.3% in June.

Unemployment among recently returned veterans, already in double digits, is poised to get worse as more soldiers return from Iraq and Afghanistan.

The jobless rate for veterans who served at any time since September 2001 — called Gulf War-era II veterans — was 13.3% in June, up from 12.1% the month before, according to the Bureau of Labor Statistics. In June 2010 it was 11.5%.

The difficulties veterans face in finding work was in evidence Sunday at the Hiring Our Heroes job fair at Sony Pictures Studios in Culver City, where more than 1,000 veterans converged to meet with employers and seek work. The veterans also got a peek at newlyweds Prince William and Catherine, who dropped by the fair as part of their tour of the Golden State.

"It just so happens that there are a lot of people out there and there aren't enough jobs," said Pavel Ksendz, a 25-year-old Culver City resident who joined the Army in 2003, right after graduating from high school. After serving for four years, including 14 months in Iraq, Ksendz recently applied for a job as a janitor in Santa Monica, only to be told there were 59 other applicants.

Veterans face a unique set of obstacles when they start to look for work, said Lance Holbrook, a veterans representative at the One-Stop Career Center in Lancaster. Many went into service straight out of high school, and although they may have experience fixing airplanes or leading people, they don't have the college degrees that employers are seeking, Holbrook said. "Most employers won't even consider them without a degree," said Holbrook, who said he's seen a surge in newly returned veterans looking for jobs in the last two months.

Unemployment among veterans could rise even more in upcoming months as more troops return from overseas. President Obama announced plans last month to pull 10,000 troops from Afghanistan by year's end and a total of 33,000 by September 2012. And the number of U.S. troops in Iraq is about 46,000 now, down from the peak of 166,000 in 2007. Most of the remaining troops will leave Iraq by year's end.

There were roughly 200,000 more veterans in the labor force this June than there were a year earlier, according to the Bureau of Labor Statistics.

"You're going to see the number grow," said Kevin Schmiegel, a veteran who works at the U.S. Chamber of Commerce on veteran employment issues and helped organize the job fair. "That's why it's so important to proactively address the issue before it becomes a larger problem."

The job fair featured dozens of booths where Sony, Target, Amazon and other companies gave out key chains, candy and pens, but many weren't accepting resumes from potential applicants.

Miguel Madrigal, a 27-year-old who served in both Iraq and Afghanistan and was awarded the Silver Star, came to the fair to find a job to help support his wife and three children when he gets out of the Marines in September.

"In the Marines, I learned loyalty, motivation, teamwork and tolerance," he said as he walked up to a booth where Waste Management representatives were handing out business cards. He introduced himself with a firm handshake and inquired about the company and positions available. But the company wasn't accepting resumes, and the representative instead handed Madrigal a sheet referring him to a website.

Jobs are hard to come by in this economy. Employers added just 18,000 net jobs in June, and the nation's unemployment rate ticked up for the third straight month, to 9.2%. The situation is even more dire in California, which had an 11.7% unemployment rate in May. The state's June figures will be released later this month.

Cherlene Emfinger, dressed in a smart white blazer and skirt and black heels, said not even her degree has helped her land a job. Emfinger, who got out of the Navy in 2007 after serving for seven years as an aviation electrician, just received a bachelor's degree from Cal State Northridge.

Emfinger has started applying for administrative assistant positions, after initially setting her sights on entry-level management jobs. She and her husband, who was also in the military, are barely making ends meet. They are only a few weeks away from falling behind on payments for their two cars, she said.

"At first I was optimistic. I have almost nine years of work history, a bachelor's degree, management skills and discipline," she said. "But now I'm just really frustrated. It doesn't make any sense."